Problem: Simplify the following expression: $ q = \dfrac{5}{9} + \dfrac{-6k - 6}{9k} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9k}{9k}$ $ \dfrac{5}{9} \times \dfrac{9k}{9k} = \dfrac{45k}{81k} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-6k - 6}{9k} \times \dfrac{9}{9} = \dfrac{-54k - 54}{81k} $ Therefore $ q = \dfrac{45k}{81k} + \dfrac{-54k - 54}{81k} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{45k - 54k - 54}{81k} $ $q = \dfrac{-9k - 54}{81k}$ Simplify the expression by dividing the numerator and denominator by 9: $q = \dfrac{-k - 6}{9k}$